Here's the original poem, written by Sheldon Alan "Shel" Silverstein. One interesting guy. He wrote and drew cartoons for Playboy, along with being well known for his children's books.

The Unicorn

A long time ago, when the earth was green
and there was more kinds of animals than you've ever seen,
and they run around free while the world was bein' born,
and the loveliest of all was the Unicorn.

There was green alligators and long-neck geese.
There was humpy bumpy camels and chimpanzees.
There was catsandratsandelephants, but sure as you're born
the lovliest of all was the Unicorn.

But the Lord seen some sinnin', and it caused him pain.
He says, "Stand back, I'm gonna make it rain."
He says, "Hey Brother Noah, I'll tell ya whatcha do.
Go and build me a floatin' zoo.

And you take two alligators and a couple of geese,
two humpy bumpy camels and two chimpanzees.
Take two catsandratsandelephants, but sure as you're born,
Noah, don't you forget my Unicorn."

Now Noah was there, he answered the callin'
and he finished up the ark just as the rain was fallin'.
He marched in the animals two by two,
and he called out as they went through,

"Hey Lord, I got your two alligators and your couple of geese,
your humpy bumpy camels and your chimpanzees.
Got your catsandratsandelephants - but Lord, I'm so forlorn
'cause I just don't see no Unicorn."

Ol' Noah looked out through the drivin' rain
but the Unicorns were hidin', playin' silly games.
They were kickin' and splashin' in the misty morn,
oh them silly Unicorn.

Then the goat started goatin', and the snake started snakin',
the elephant started elephantin', and the boat started shaking'.
The mouse started squeakin', and the lion started roarin',
and everyone's aboard but the Unicorn.

I mean the green alligators and the long-neck geese,
the humpy bumpy camels and the chimpanzees.
Noah cried, "Close the door 'cause the rain is pourin' -
and we just can't wait for them Unicorn."

Then the ark started movin', and it drifted with the tide,
and the Unicorns looked up from the rock and cried.
And the water come up and sort of floated them away -
that's why you've never seen a Unicorn to this day.

You'll see a lot of alligators and a whole mess of geese.
You'll see humpy bumpy camels and lots of chimpanzees.
You'll see catsandratsandelephants, but sure as you're born
you're never gonna see no Unicorn.